I’m not experienced enough to say whether getting the entire container out of the storage pool and into another container is workable, but providing the file system in very messed up, we should be able to get specific data, e.g. MySQL data and logs, or a user’s home directory.
I created a BTRFS loopback storage pool device and a container on it, and was able to mount the IMG and drill down into the file system mount point to get the test file created in the container.
mount -vt btrfs -o loop /var/snap/lxd/common/lxd/disks/{yourdisk}.img /{mount-point}
e.g.
mount -vt btrfs -o loop /var/snap/lxd/common/lxd/disks/btrfsloop1.img /mnt
cp /mnt/containers/btrfstest1/rootfs/root/btrfstest1.txt /home/someuser/restore/
It would be interesting to see whether the above mount will work in your scenario.